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LunaCalc

Statistics

Sample Size Calculator

Estimate sample size from confidence level, margin and proportion.

Calculator
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About this calculator

This sample size calculator tells you how many responses a survey needs for a target margin of error at a given confidence level.

Formula notes

n = z²·p(1−p) / e². With p = 0.5 for the conservative maximum.

Worked examples

  1. Example: 95% confidence and ±5% margin gives n = 1.96²·0.25 / 0.0025 ≈ 385 respondents.
  2. At 95% confidence, 5% margin, and expected proportion 50%, the large-population estimate is about 385 completed responses.

How to use it

  1. Choose the confidence level.
  2. Set the margin of error you can tolerate.
  3. Read the minimum sample size, rounding up.

Frequently asked questions

Why is the classic answer 385?

1.96² × 0.25 / 0.05² = 384.16, which rounds up to 385.

What if I expect a skewed proportion?

Replace p = 0.5 with your expected value; n will drop because p(1−p) shrinks.

Limits and interpretation

  • The calculation assumes a probability sample and addresses sampling precision, not response rate, design effects, clustering, or bias.
  • Required invitations usually exceed completed sample size, and subgroup analysis may require larger targets.

References